Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int N, M, MIN = 2140000000, Mat[105][105], Min[105], resp = 0, Sum = 0;
struct ans {
  int part, type;
} v[105 * 105 * 105 * 5];
int main() {
  cin >> N >> M;
  for (int i = 1; i <= N; i++)
    for (int j = 1; j <= M; j++)
      cin >> Mat[i][j], Sum += Mat[i][j], MIN = min(MIN, Mat[i][j]);
  if (MIN > 0) {
    if (N > M)
      for (int i = 1; i <= MIN; i++)
        for (int j = 1; j <= M; j++)
          v[++resp].part = j, v[resp].type = 2, Sum -= N;
    else
      for (int i = 1; i <= MIN; i++)
        for (int j = 1; j <= N; j++)
          v[++resp].part = j, v[resp].type = 1, Sum -= M;
    for (int i = 1; i <= N; i++)
      for (int j = 1; j <= M; j++) Mat[i][j] -= MIN;
  }
  for (int i = 1; i <= N; i++) Min[i] = 2140000000;
  for (int i = 1; i <= N; i++)
    for (int j = 1; j <= M; j++) Min[i] = min(Min[i], Mat[i][j]);
  for (int i = 1; i <= N; i++) {
    for (int j = 1; j <= Min[i]; j++) v[++resp].part = i, v[resp].type = 1;
    for (int j = 1; j <= M; j++) Mat[i][j] -= Min[i];
    Sum -= Min[i] * M;
  }
  for (int i = 1; i <= M; i++) Min[i] = 2140000000;
  for (int i = 1; i <= N; i++)
    for (int j = 1; j <= M; j++) Min[j] = min(Min[j], Mat[i][j]);
  for (int i = 1; i <= M; i++) {
    for (int j = 1; j <= Min[i]; j++) v[++resp].part = i, v[resp].type = 2;
    for (int j = 1; j <= N; j++) Mat[i][j] -= Min[i];
    Sum -= Min[i] * N;
  }
  if (Sum > 0)
    cout << -1;
  else {
    cout << resp << '\n';
    for (int i = 1; i <= resp; i++) {
      if (v[i].type == 1)
        cout << "row ";
      else
        cout << "col ";
      cout << v[i].part << "\n";
    }
  }
  return 0;
}